Leonid Monin, Department of Mathematics, University of Toronto, Toronto, ON Canada M5S 2E4 e-mail: lmonin@math.toronto.edu

Abstract/Résumé:

In this paper the geometry of the lattice is used to prove basic theorems about subgroups and factor groups of \(\Bbb Z^n\). We suggest a geometric algorithm which reduces a finitely generated abelian group to its normal form.

Dans ce papier, un argument de géométrie sur les réseaux est utilisé pour prouver des théorèmes fondamentaux sur les sous-groupes ou les groupes quotients de \(\Bbb Z^n\). Nous proposons un algorithme géométrique qui réduit un groupe abélien finement engendré à sa forme normale.

Keywords: Integer lattice, Integer volume, Normal Smith form

AMS Subject Classification: Lattice polytopes (including relations with commutative algebra and algebraic geometry) 52B20

PDF(click to download): Lattice Geometry and Reduction of Finitely Generated Abelian Groups to a Normal Form